The Church-Rosser property in symmetric combinatory logic
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The Church-Rosser property in symmetric combinatory logic
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| Id. |
1445170 |
| Idioma |
inglés
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| Titulo |
The Church-Rosser property in symmetric combinatory logic |
| Autor(es) |
Bimbó, Katalin
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| Localización |
http://projecteuclid.org/euclid.jsl/1120224727
J. Symbolic Logic 70, iss. 2 (2005), 536-556
doi:10.2178/jsl/1120224727
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| Versión |
1.0 |
| Estado |
Final
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| Descripción |
Symmetic combinatory logic with the symmetric analogue of a combinatorially
complete base (in the form of symmetric ?-calculus) is known to lack
the Church-Rosser property. We prove a much stronger theorem that
no symmetric combinatory logic that contains at least two proper
symmetric combinators has the Church-Rosser property. Although the
statement of the result looks similar to an earlier one concerning
dual combinatory logic, the proof is different because symmetric
combinators may form redexes in both left and right associated terms.
Perhaps surprisingly, we are also able to show that certain symmetric
combinatory logics that include just one particular constant are
not confluent. This result (beyond other differences) clearly sets
apart symmetric combinatory logic from dual combinatory logic, since
all dual combinatory systems with a single combinator or a single dual
combinator are Church-Rosser. Lastly, we prove that a symmetric
combinatory logic that contains the fixed point and the one-place
identity combinator has the Church-Rosser property.
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| Tipo |
application/pdf
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| Palabras clave |
symmetric combinatory logic
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| Tipo de recurso |
Text
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| Tipo de Interactividad |
Expositivo
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| Nivel de Interactividad |
muy bajo
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| Audiencia |
Estudiante
Profesor
Autor
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| Estructura |
Atomic |
| Coste |
no
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| Copyright |
sí
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Copyright 2005 Association for Symbolic Logic |
| Formatos |
application/pdf
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| Requerimientos técnicos |
Browser: Any
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| Fecha de contribución |
19-sep-2008 |
| Contacto |
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